Despite my etymythology alarm sounding, this one seems to be true. Adrianna Orr of the OED did a nice write up on how she uncovered the origin.
The OED3 entry itself, however, is very conservative, stating:
Origin uncertain. Perhaps <Mexican Spanish Nacho, pet-form of the male forename Ignacio (with reference to the supposed creator of the dish: see note below).
A Mexican chef, Ignacio (‘Nacho’) Anaya, who worked in the Piedras Negras area in the 1940s, is often credited with creating the first nachos (see e.g. quot. 1970).]
I think they could safely upgrade this to a “probably” and still be on the conservative side.
Dishes are commonly named after the chef’s who create them (e.g., Cesar salad), but claims for invention and individual naming are always suspect. So skepticism is usually warranted, but should not be unduly applied.
[Pipped by languagehat]
Also note these earlier cites:
1948 San Antonio (Texas) Light 28 Jan. 14A (advt.) Latin Quarter Mexican Restaurant...”Nachos” (Mexican Hors-D’-Oeuvres)...35c Here is a real dainty! Golden fried tortilla strips, deliciously spiced, topped with mellow, melted cheese and garnished with chili jalapeno bits. 1949 J. TRAHEY Taste of Texas 27 He returned carrying a large dish of Nachos Especiales. “These Nachos,” said Pedro, “will help El Capitan—soon he will forget his troubles for nachos make one romantic.”
The early San Antonio appearance and the phrase Nachos Especiales support the origin story.